new battery,starter, transmission lock out.

Sounds like a slipping timing belt.

if all this is new and your sure its good its possible the starter relay is going bad on it,that will cause it to do this , l am not sure of the exact location of the one on that car,but that is what they do when they go bad,or start going bad,a bad ignition switch will also do the very same thing,good luck with it.

You need to find a shop with a computer scan tool that has the capability to graph all the sensors when your engine is running. NEVER replace a part till you know the problem. Get is very expensive and may not solve the problem There are a lot of things that could cause this problem.

Give me some more info so l can tell you exactly what to do.

Well l guess it is not a pressing issue.

The relay is under the drivers kick panel behind the fuse box, this is a possibility, my question is; does this car have an automatic transmission?

From my experience on SAAB is is the gear range selector (safety neutral switch) is the problem. When the car gets to operating temp. & u shut of the car, the switch gets an open circuit from the expansion on the metal & the car wo not crank until the car cools down & will start fine until it is hot again. When the car cools down it makes contact & starts

Whether the car is a manual or automatic transmission, it could be the relay or ignition switch.

YOU SHOULD GET THE VEHICLES COMPUTER SCANNED AND CHECK FOR ANY PROBLEMS AS WELL AS CODES AND THEN YOU WILL HAVE A GOOD IDEA ON WHAT THE PROBLEM TRULY IS.

TRY FINDING AN INDEPENDENT SHOP INSTEAD OF THE DEALER OR A CHAIN STORE BECAUSE YOU WILL BE OVERALL MORE PLEASED WITH THE FINDINGS AND THE SERVICE.

LEAVE IT THERE WITH THEM SO THAT THEY CAN FIND THE PROBLEM FOR YOU, IT WILL BE A LOT BETTER THAN JUST REPLACING PART AFTER PART AND NOT DOING ANY GOOD.